Question

1. \\( \triangle mno \cong \\) ?

(a) \\( \triangle mpo \\)
b. \\( \triangle omp \\)
c. \\( \triangle mop \\)
d. not \\( \cong \\)

1. \\( \triangle hij \cong \\) ?

a. \\( \triangle hik \\)
(b) \\( \triangle ihk \\)
c. \\( \triangle kih \\)
d. not \\( \cong \\)
for # 10 - 12, match the correct reason to the congruent triangles.
a) sas b) sss c) aas d) asa e) hl f) not \\( \cong \\)
10)
11)
12)

Explanation:

8)

Step1: Analyze triangle congruence

In \(\triangle MNO\) and \(\triangle MPO\), \(NM = MP\) (given by the tick marks), \(\angle NMO=\angle PMO = 90^{\circ}\), and \(OM\) is common. By the Side - Angle - Side (SAS) congruence criterion, \(\triangle MNO\cong\triangle MPO\).

9)

Step1: Analyze triangle congruence

In \(\triangle HIJ\) and \(\triangle IHK\), \(\angle K=\angle J\) (given by the arc marks), \(\angle HIK=\angle JIH\) (common angle), and \(HI\) is common. By the Angle - Angle - Side (AAS) congruence criterion, \(\triangle HIJ\cong\triangle IHK\).

10)

Step1: Identify congruence criterion

In \(\triangle HIK\) and \(\triangle IHJ\), \(\angle K=\angle J\) (arc marks), \(\angle HIK=\angle JIH\) (common angle), and \(HI\) is common. This satisfies the AAS (Angle - Angle - Side) congruence criterion.

11)

Step1: Identify congruence criterion

In \(\triangle FMR\) and \(\triangle EDR\), \(FM = ED\) (tick marks), \(MR = DR\) (double - tick marks), and \(\angle FRM=\angle ERD\) (vertically opposite angles). By the SAS (Side - Angle - Side) congruence criterion.

12)

Step1: Identify congruence criterion

In \(\triangle MNO\) and \(\triangle MPO\), \(NM = MP\) (tick marks), \(\angle NMO=\angle PMO = 90^{\circ}\), and \(OM\) is common. By the HL (Hypotenuse - Leg) congruence criterion for right - angled triangles.

Answer:

1. a. \(\triangle MPO\)
2. b. \(\triangle IHK\)
3. C) AAS
4. A) SAS
5. E) HL